The point is the following:

Delta, $\Delta$, is defined as $\frac{\partial C}{\partial S}$, where $C$ is the value of the call option, and $S$ is the price of the underlying asset.

So, given that the value of a call option for a non-dividend-paying underlying stock in terms of the Black–Scholes parameters is

$$C = N(d_{1})S - N(d_{2})Ke^{-rT},$$

$$\Delta = \frac{\partial C}{\partial S} = N(d_{1}).$$

Basically, Delta is just the first partial derivative of $C$ with respect to $S$.